Wifi is free as it uses a wireless router elsewhere, not the phone network :? If you was to use your wireless router at home, it does not cost you anything!
Or do you mean Wifi when you are out and about? If so, this can vary. It depends on who has the main router. I spose they can charge a fee for it?

If you use wifi like BT Openzone or the cloud while out and about they will charge you, but from home or any other wifi you have access to it should be free. You can also get free wifi in certain pub chains and most McDonalds and some burger kings

Wifi is free as it uses a wireless router elsewhere, not the phone network :? If you was to use your wireless router at home, it does not cost you anything!
Or do you mean Wifi when you are out and about? If so, this can vary. It depends on who has the main router. I spose they can charge a fee for it?

Im on about home router and also when im in mcdonals and weatherspoons (they say free but i was told id still be charged?)

Using the phone over wifi is just the same as using your PC over the same wifi connection, using a public one such as at McDonalds or a pub you may pay a fee to the local place (not the network) - usually if it's not free when you try to browse you'll be taken to a page to organise payment or enter an access code.

Some companies will offer you some bundled time with the likes of BT Openzone or T-mobile's wi-fi system although as you've not mentioned what network or tariff you're on we can only guess.